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Brackets Factors and Equations

This exercise set focuses on expanding and simplifying expressions with brackets and factors, as well as solving equations. It includes oral examples and written exercises.

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Brackets Factors and Equations

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  1. Brackets Factors and Equations Exercises 1 and 2

  2. Oral Examples: Expand • p(q + r) • p(q - r) • -p(q + r) • -p(q - r)

  3. Oral Examples: Expand • 5(2 + y) • 5(2 - y) • -5(2 + y) • -5(2 - y)

  4. Oral Examples: Expand • 5(3x + 4y) • 5(3x - 4y) • -5(3x + 4y) • -5(2 - y)

  5. Exercise 1: Expand 1. 2(x + 3) 2. 2(x - 3) • -2(x + 3) 4. -2(x - 3)

  6. Exercise 1: Expand 1. 2(x + 3) = 2x + 6 2. 2(x - 3) = 2x - 6 • -2(x + 3) = -2x - 6 4. -2(x - 3) = -2x + 3

  7. Exercise 1: Expand 5. 3(2 + y) • 3(2 - y) • -3(2 + y) 8. -3(2 - y)

  8. Exercise 1: Expand 5. 3(2 + y) = 6 + 3y • 3(2 - y) = 6 – 3y • -3(2 + y) = -6-3y • -3(2 - y) = -6 +3y

  9. Expand 9. 3(x + 4) 10. -3(x + 4) 11. 3(x - 4) 12. -3(x - 4)

  10. Expand 9. 3(x + 4) = 3x + 12 10. -3(x + 4) = -3x - 12 11. 3(x - 4) = 3x - 12 12. -3(x - 4) = -3x + 12

  11. Exercise 1: Expand 13. 4(3 + y) 14. -4(3 + y) 15. 4(3 - y) 16. -4(3 - y)

  12. Exercise 1: Expand 13. 4(3 + y) = 12 + 4y 14. -4(3 + y) = -12 – 4y 15. 4(3 - y) = 12 – 4y 16. -4(3 - y) = -12 + 4y

  13. Exercise 1: Expand 17. 4(x + 2) 18. 4(x - 2) 19. -4(x + 2) 20. -4(x - 2)

  14. Exercise 1: Expand 17. 4(x + 2) = 4x + 8 18. 4(x - 2) = 4x - 8 19. -4(x + 2) = -4x - 8 20. -4(x - 2) = -4x + 8

  15. Exercise 1: Expand 21. 2(x + 4) 22. 2(x - 4) 23. -2(x + 4) 24. -2(x - 4)

  16. Exercise 1: Expand 21. 2(x + 4) = 2x + 8 22. 2(x - 4) = 2x - 8 23. -2(x + 4) = -2x - 8 24. -2(x - 4) = -2x + 8

  17. Exercise 1: Expand 25. 5(x + y) 26. -5(x + y) 27. 5(x - y) 28. -5(x - y)

  18. Exercise 1: Expand 25. 5(x + y) = 5x + 5y 26. -5(x + y) = -5x – 5y 27. 5(x - y) = 5x – 5y 28. -5(x - y) = -5x + 5y

  19. Exercise1: Expand 29. 2(3x + 5y) 30. -2(3x + 5y) 31. 2(3x - 5y) 32. -2(3x - 5y)

  20. Exercise1: Expand 29. 2(3x + 5y) = 6x + 10y 30. -2(3x + 5y) = -6x -10y 31. 2(3x - 5y) = 6x -10y 32. -2(3x - 5y) = -6x +10y

  21. Exercise 1: Expand 33. 3(4x + 5y) 34. 3(4x - 5y) 35. -3(4x + 5y) 36. -3(4x - 5y)

  22. Exercise 1: Expand 33. 3(4x + 5y) =12x + 15y 34. 3(4x - 5y) = 12x -15y 35. -3(4x + 5y) = -12x – 15y 36. -3(4x - 5y) = -12x + 15y

  23. Exercise 1: Expand 37. 4(2x + 5y) 38. 4(2x - 5y) 39. -4(2x + 5y) 40. -4(2x - 5y)

  24. Exercise 1: Expand 37. 4(2x + 5y) = 8x + 20y 38. 4(2x - 5y) = 8x – 20y 39. -4(2x + 5y) = -8x – 20y 40. -4(2x - 5y) = -8x + 20y

  25. Exercise 2 1. x (x + 1) 2. x (x - 2) 3. x (x + 3) 4. x (x - 4) 5. y (1 + y) 6. y (2 - y)

  26. Exercise 2 1. x (x + 1) = x2 + x 2. x (x - 2) = x2 - 2x 3. x (x + 3) = x2 + 3x 4. x (x - 4) = x2 - 4x 5. y (1 + y) = y + y2 6. y (2 – y)= 2y – y2

  27. Exercise 2 7. y (3 + y) 8. y (4 - y) 9. x (x + y) 10. x (x - y) 11. y (x + y) 12. y (x - y)

  28. Exercise 2 7. y (3 + y) = 3y + y2 8. y (4 - y) = 4y- y2 9. x (x + y) = x2 + xy 10. x (x - y) = x2 - xy 11. y (x + y) = xy + y2 12. y (x - y) = xy + y2

  29. Exercise 2 13. 2x (x + 4) 14. 2x (3 + y) 15. 2x (3x + 4y) 16. 2xy (3x + 4y) 17. 3y (x - 5) 18. 3y (4 - y)

  30. Exercise 2 13. 2x (x + 4) = 2x2 + 8x 14. 2x (3 + y) = 6x + 2xy 15. 2x (3x + 4y) = 6x2 +8xy 16. 2xy (3x + 4y) = 6x2y + 8xy2 17. 3y (x - 5) = 3xy – 15y 18. 3y (4 - y) = 12y – 12y2

  31. Exercise 2 19. 3y (4x - 5y) 20. 3xy (4x - 5y) 21. 4x (x + 2) 22. 4x (5 + y) 23. 4x (5x + 2y) 24. 4xy (5x + 2y)

  32. Exercise 2 19. 3y (4x - 5y) = 12xy – 15y2 20. 3xy (4x - 5y) = 12x2y – 15xy2 21. 4x (x + 2) = 4x2 +8x 22. 4x (5 + y) = 20x + 4xy 23. 4x (5x + 2y) = 20x2 + 8xy 24. 4xy (5x + 2y) = 20x2y + 8xy2

  33. Exercise 2 25. 5y ( x - 3) 26. 5y (2 - y) 27. 5y (2 - 3y) 28. 5y (2 - 3y) 29. x (x + 4) + 2(x + 4) 30. y (y + 1) + 3(y + 1)

  34. Exercise 2 25. 5y ( x - 3) = 5xy – 15y 26. 5y (2 - y) = 10y – 5y2 27. 5y (2 - 3y) = 10y – 15y2 28. 5y (2 - 3y) = 10y – 15y2 29. x (x + 4) + 2(x + 4) = x2 + 6x + 8 30. y (y + 1) + 3(y + 1) = y2 + 4y + 3

  35. Exercise 2 31. x (x + 2) + (x + 2) 32. y (y + 3) + 4(y + 3) 33. x (x + 3) + 2(x + 3) 34. y (y + 4) + (y + 4) 35. x (x - 4) + 2(x - 4) 36. y (y - 1) + 3(y - 1)

  36. Exercise 2 31. x (x + 2) + (x + 2) 32. y (y + 3) + 4(y + 3) 33. x (x + 3) + 2(x + 3) 34. y (y + 4) + (y + 4) 35. x (x - 4) + 2(x - 4) 36. y (y - 1) + 3(y - 1)

  37. 37. x (x - 2) + (x - 2) • 38. y (y - 3) + 4(y - 3) • 39. x (x - 3) + 2(x - 3) • 40. y (y - 4) + (y - 4) • 41. x (x + 4) - 2(x + 4) • 42. y (y + 1) - 3(y + 1)

  38. 43. x (x + 2) - (x + 2) • 44. y (y + 3) - 4(y + 3) • 45. x (x + 3) - 2(x + 3) • 46. y (y + 4) - (y + 4) • 47. x (x - 4) - 2(x - 4) • 48. y (y - 1) - 3(y - 1)

  39. 49. x (x - 2) - (x - 2) • 50. y (y - 3) - 4(y - 3) • 51. x (x - 3) - 2(x - 3) • 52. y (y - 4) - (y - 4) • 53. 3x (x + 2) + 4(x + 2) • 54. 3x (x - 2) + 4(x - 2)

  40. 55. 3x (x + 2) - 4(x + 2) • 56. 3x (x - 2) - 4(x - 2) • 57. 2y (y + 4) + 3(y + 4) • 58. 2y (y - 4) + 3(y - 4) • 59. 2y (y + 4) - 3(y + 4) • 60. 2y (y - 4) - 3(y - 4)

  41. 61. 2x (x + 3) + (x + 3) • 62. 2x (x - 3) + (x - 3) • 63. 2x (x + 3) - (x + 3) • 64. 2x (x - 3) - (x - 3)

  42. Exercise 3 • 1. 2x + 6y = 2 ( ) • 2. 3x - 6y = 3 ( ) • 3. 8x + 2y = 2 ( ) • 4. 8x - 4y = 4 ( ) • 5. 3x + 12 = 3 ( ) • 6. 12x - 4 = 4 ( )

  43. Factorise • 7. 30 + 5y = 5 ( ) • 8. 6 - 30y = 6 ( ) • 9. 4x + 6y = 2 ( ) • 10. 6x - 9y = 3 ( ) • 11. 10x + 8 = 2 ( ) • 12. 15x - 12 = 3 ( )

  44. Factorise • 13. 8 + 12y = 4 ( ) • 14. 20 - 24y = 4 ( ) • 15. 12x + 18y - 30z = 6 ( ) • 16. 18x - 24y + 30z = 6 ( )

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